Well, do you know for certain that it was your puppy that bit him? Could another animal have bit him? What country are you from? Some countries are more prone to Rabies because they don't get their animals vaccinated as much. Yes it would be soon enough to get the puppy vaccinated. But if you know you saw the puppy bite or scratch him and that it couldn't have been from another animal that is good. But do you know if your animal has ever been left alone outside? If so then you don't know for sure that the puppy didn't get bitten by another animal. It is unlikely though if the fencing is really tight and high up but we get rats and other rodents coming in our back yard and it has a 6 foot fence all around. It is possible that the puppy could have been exposed that way? You should get him the shots the day of exposure so if you have any doubts you have to do it now. People and animals don't show symptoms until it is too late to treat them.
Most likely it isn't rabies, however if you are worried, get the shots. Your puppy can be vaccinated against rabies at as early at 12 weeks old. Go ahead and gave that done. In my state if a person is bitten by an animal that hasn't been vaccinated, and is taken to the doctor, they are required to report to the health department. Which then in turns, contacts the owner of the animal and requires they quarantine the animal for 10 days. Good luck.